The availability of an accurate model for RNA tertiary folding can greatly aid in our understanding of RNA functions and in RNA-targeted drug discovery. However, unlike the protein folding problem which has been extensively studied for decades, modeling of tertiary RNA folding is a relatively new field of endeavor. Our current graph-theoretic thermodynamic model has allowed us to make better predictions than other existing models on RNA secondary structure melting curves. In this proposal, we aim to move beyond the secondary structure model to study tertiary RNA folding. A key advantage of our approach is the completeness and certainty in our conformational sampling. Incomplete conformational sampling may result in unacceptable loss of accuracy. Our thermodynamic and kinetic models will be developed in parallel in this project. The thermodynamic model, in which user can supply energy parameters, will enable us to extract parameters for RNA tertiary interactions from experimental melting curves. Since the first submission of this proposal, we have generated new results indicating that we can accurately capture tertiary folds and off-lattice conformations to give reliable partition functions. The kinetic model will be developed using a master equation approach, which we have successfully used to treat RNA hairpin folding kinetics. Our long-term goal is to move beyond hairpin to treat large complex RNAs. Our immediate goal is to remove two key "roadblocks" on the road toward our long-term goal: to search for transition states from rate equations, and to reduce the rate equations by conformational clustering. Experimental tests will focus on a series of rationally designed RNA systems. A key point is that the experiments will be performed under exactly the same salt condition used in theoretical predictions.